Home › Collection › Sections › Plane section of a solid

Plane section of a solid

Cut the solid (octahedron) with the plane of normal (0, 0, 1) through P(7, 7, 2). Find the section and its true shape.

Step-by-step solution

1. Find the intersection of the plane with each face of the solid.
2. Join the cutting points in order: the section is the resulting convex polygon.
3. To see it in true shape, rotate the cutting plane onto a projection plane.
4. Check the edge cases: tangent plane (one point) or outside plane (no section).

Result: section with 4 vertices; area 8 u² and perimeter 11.31 u.

If the plane is projecting, the section looks like a segment in the edge-on view; the points are carried to the other view.

PractiseBack to the block